A049572 Primes p such that x^40 = 2 has a solution mod p.

2, 7, 23, 47, 73, 79, 89, 103, 127, 151, 167, 199, 223, 233, 239, 257, 263, 337, 359, 367, 383, 431, 439, 463, 479, 487, 503, 599, 607, 647, 719, 727, 743, 823, 839, 863, 887, 911, 919, 937, 967, 983, 1039, 1063, 1087, 1103, 1217, 1223, 1249, 1279, 1289

Offset

1,1

Comments

Complement of A059352 relative to A000040. - Vincenzo Librandi, Sep 14 2012

Links

R. J. Mathar, Table of n, a(n) for n = 1..1000

Index entries for related sequences

Example

0^40 == 2 (mod 2). 2^40 == 2 (mod 7). 3^40 == 2 (mod 23). 3^40 == 2 (mod 47). 18^40 == 2 (mod 73). 2^40 == 2 (mod 79). 11^40 == 2 (mod 89). 44^40 == 2 (mod 103). - R. J. Mathar, Jul 20 2025

Mathematica

ok[p_]:= Reduce[Mod[x^40 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[300]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(1300) | exists(t){x : x in ResidueClassRing(p) | x^40 eq 2}]; // Vincenzo Librandi, Sep 14 2012

Crossrefs

Cf. A000040, A059352.

Sequence in context: A049232 A100917 A049552 * A094786 A028871 A053705

Adjacent sequences: A049569 A049570 A049571 * A049573 A049574 A049575

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved